When the Conservatives were booted out of office in 1997 the party was left with no MPs in Scotland. Today they have one – a total which few expect to rise in 2015.

Explanations abound for the Tories’ Scottish decline, economic and cultural as well as political. One of the most common is that they are still being punished for the legacy of Mrs Thatcher and what she “did to” Scotland. But this theory does not ring true. For one thing, the Conservatives’ popularity in Scotland has been waning since 1955, when they were the largest party. For another thing, when the supposedly wickedly anti-Scottish Thatcher was in Number 10, the Tories won more seats and more votes in Scotland than they have ever done since. And for a third thing, even if Mrs Thatcher were universally reviled in Scotland – which she is not – I do not believe that most Scots are so unimaginative as to vote according to what they thought of the Prime Minister before the Prime Minister before the Prime Minister before last.

Whatever the history, the task for the Conservatives is to work out where they are now and what they can do about it. Over the last eight months, I have looked into the question with a 10,000-sample poll, plus focus groups and follow-up surveys. My full report, Cameron’s Caledonian Conundrum, is published today.

Despite the party’s shrinking vote share, there are potential Tories at large in Scotland. As well as the small “Tory Core” – loyal Conservatives who always turn out – I found a group of what I have called “Reluctant Cameroons”. These people, one in six of the Scottish electorate, are attracted to David Cameron and trust the Tories on the economy, but most say they would not vote Conservative tomorrow. Another one in ten falls into the “Willing to Listen” group, who currently lean towards Labour despite preferring Cameron as Prime Minister, though many are undecided.

The Conservative Party holds three main attractions for its target voters: they prefer Cameron as Prime Minister; they see the Tories as willing to take tough decisions; and they trust the Tory team over Miliband and Balls to manage the economy.

At the same time, they see three big drawbacks. First, like many in England, they doubt the Tories are really on the side of people like them. Second, they do not feel the party cares much about Scotland, and has little enthusiasm for devolution. Finally, they consider the Tories effectively irrelevant in Scottish elections. Many who would support the Conservatives if they lived in England instead vote to try to keep out whichever of Labour or the SNP they believe to be more disastrous.

What can the Tories do about all this? First of all, they must show they are in touch with people’s anxieties and aspirations as they are today. This means campaigning on health, public services and housing as well as constitutional issues and the deficit, and understanding that the benefits of an economic recovery seem remote to many people.

Like David Cameron, Ruth Davidson is an asset here. If she has yet to make a big impression on Scottish voters, she is not alone: neither has Johann Lamont nor Willie Rennie. The swing voters we spoke to had a generally positive view of her – and if the thing that most stuck in their minds was that she had been asked for ID when trying to buy a beer at a Springsteen gig at Hampden Park, this at least proves her to be the antithesis of the hunting-shooting-fishing caricature of the Scots Tory.

But how to show the Tories will stand up for Scotland? Picking a fight over policy with Cameron might demonstrate independence from London, but in so doing it could decouple the Scottish Conservatives from what is, in voters’ eyes, their main source of credibility. Scots who want a party of opposition already have plenty of options.

Rather than trying to stand up for Scotland against Westminster, Tories need to stand up for Scotland in Westminster. Among other things, this will mean more campaign support and more attention given to the effects in Scotland of national policy decisions.

In Holyrood elections, the problem of the Tories’ irrelevance is not just the self-fulfilling one of people not voting for them because they won’t win. For the people willing to give them a hearing, the point of the party is to make hard choices in the national interest. But as they see it, those choices are currently being made in Westminster. Many feel Holyrood’s job is to wave the flag and hand out the money. What need is there for a nettle-grasping party where there are no nettles to be grasped?

This would change in a Scottish Parliament fully responsible for everything it raised and spent. In such a situation, I found, Scottish voters would expect an increase in spending and debt with no corresponding improvement in public services. They would need someone to make sure the books were balanced.

Ironically enough, this need would be greatest of all in an independent Scotland – which of course the Tories will vigorously oppose. But if the Scots vote to keep the Union, more powers for Edinburgh could be to the party’s political advantage. As long as voters think the Scottish Parliament exists to sign the cheques, while the fiscal prudence happens elsewhere, the Conservatives will seem redundant. In other words, nothing would show the need for Tories in Holyrood like a dose of Devo Plus.

Ultimately, there are two overlapping routes to a Tory revival in Scotland: helping to shape more independent Scottish institutions where voters will see a role for the Conservatives; and showing the party takes the Union as seriously as it claims to.

If it sounds like a hopeless cause, consider London. In 1997 the Conservatives won just 11 of the capital’s 74 seats, 19 points behind Labour in the popular vote. A city renowned for its liberal tendencies was given a degree of self-government, and promptly elected, then re-elected, an anti-establishment leader from the left. But what happened next?